Need help with calculus

Question 1(Multiple Choice Worth 4 points)

The slope of the tangent line to a curve at any point (x, y) on the curve is. What is the equation of the curve if (4, 1) is a point on the curve?

x2 y2= 15x2+ y2= 15x + y = 15xy = 15

Question 2(Multiple Choice Worth 4 points)

The particular solution of the differential equationfor which y(0) = 80 is

y = 80e2ty = 80 e0.5ty = 79 + ety = 80e0.5t

Question 3(Multiple Choice Worth 4 points)

Which of the following is the general solution of the differential equation?

y2= x2+ Cy2= 2x2+ Cy2= 4x2+ Cx2 y2= C

Question 4(Multiple Choice Worth 4 points)

The temperature of a cup of coffee varies according to Newton's Law of Cooling:, where T is the water temperature, A is the room temperature, and k is a positive constant. If the coffee cools from 180F to 100F in 10 minutes at a room temperature of 75F, how long (to the nearest minute) will it take the water to cool to 80F?

13182127

Question 5(Multiple Choice Worth 4 points)

Find the specific solution of the differential equationwith condition y(3) = e.

None of these